Solve 4/55/13-0.45/13+3/5div1.6

$$\frac{ 4 }{ 5 } \frac{ 5 }{ 13 } -0.4 \frac{ 5 }{ 13 } + \frac{ 3 }{ 5 } \div 1.6$$

Evaluate

$$-\frac{53}{520}\approx -0.101923077$$

Solution Steps

Multiply \frac{4}{5} times \frac{5}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 5}{5\times 13}-\frac{0.4\times 13+5}{13}+\frac{\frac{3}{5}}{1.6}$$

Cancel out 5 in both numerator and denominator.

$$\frac{4}{13}-\frac{0.4\times 13+5}{13}+\frac{\frac{3}{5}}{1.6}$$

Multiply 0.4 and 13 to get 5.2.

$$\frac{4}{13}-\frac{5.2+5}{13}+\frac{\frac{3}{5}}{1.6}$$

Add 5.2 and 5 to get 10.2.

$$\frac{4}{13}-\frac{10.2}{13}+\frac{\frac{3}{5}}{1.6}$$

Expand \frac{10.2}{13} by multiplying both numerator and the denominator by 10.

$$\frac{4}{13}-\frac{102}{130}+\frac{\frac{3}{5}}{1.6}$$

Reduce the fraction \frac{102}{130} to lowest terms by extracting and canceling out 2.

$$\frac{4}{13}-\frac{51}{65}+\frac{\frac{3}{5}}{1.6}$$

Least common multiple of 13 and 65 is 65. Convert \frac{4}{13} and \frac{51}{65} to fractions with denominator 65.

$$\frac{20}{65}-\frac{51}{65}+\frac{\frac{3}{5}}{1.6}$$

Since \frac{20}{65} and \frac{51}{65} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20-51}{65}+\frac{\frac{3}{5}}{1.6}$$

Subtract 51 from 20 to get -31.

$$-\frac{31}{65}+\frac{\frac{3}{5}}{1.6}$$

Express \frac{\frac{3}{5}}{1.6} as a single fraction.

$$-\frac{31}{65}+\frac{3}{5\times 1.6}$$

Multiply 5 and 1.6 to get 8.

$$-\frac{31}{65}+\frac{3}{8}$$

Least common multiple of 65 and 8 is 520. Convert -\frac{31}{65} and \frac{3}{8} to fractions with denominator 520.

$$-\frac{248}{520}+\frac{195}{520}$$

Since -\frac{248}{520} and \frac{195}{520} have the same denominator, add them by adding their numerators.

$$\frac{-248+195}{520}$$

Add -248 and 195 to get -53.

$$-\frac{53}{520}$$

Factor

$$-\frac{53}{520} = -0.10192307692307692$$